An on-demand source of nanoparticles for optomechanics Open Access

Experiments in levitated optomechanics^1–4 are driven by the desire to explore the limits of quantum mechanics^5–7 and to study single-particle thermodynamics⁸ or correlations in many body systems.⁹ Levitated optomechanics is paving the path for sensitive sensors, in the quest for dark matter,¹⁰ non-Newtonian forces,¹¹ particle physics,^3,12 and probing gravity-mediated entanglement.^13,14 Such experiments require minimizing damping and decoherence to achieve quality factors even up to $Q=1010$ for mechanical oscillation.¹⁵ This raises the question of how to generate and individualize particles with well-defined materials and sizes and how to launch them reproducibly at a good rate, on demand, and in high vacuum.

As colloidal nanoparticles have become commercially available in a wide variety of materials, sizes, and in good abundance, individualization has often been achieved using piezoactivated nebulizers.¹⁶ In addition to contaminating the vacuum chamber with a dense aerosol, nebulizers are typically operated at a pressure regime of 10–1000 mbar. Once a particle is trapped, evacuation of the experimental chamber to ultra-high vacuum may take a long time. One can overcome this limitation by transferring trapped particles via a hollow core photonic crystal fiber between two differentially pumped chambers,¹⁷ but this adds complexity to the experiment.

Glass nanobeads have been launched from a flat substrate in high vacuum using piezoelectric acceleration.¹⁸ This works even for small spheres (⁠ $r<50 nm$⁠) launched from a non-sticky surface.¹⁹ A similar effect is achieved using laser-induced acoustic desorption (LIAD), where a short laser pulse (typically with $E<10 mJ, τ<10 ns$⁠, w < 100 μm) is focused on the backside of a 10–500 μm thick silicon wafer or metal foil. The ensuing thermomechanical stress and acoustic shock on the opposing side of the sample launch the nanoparticles even in high vacuum. LIAD has been used as a source in experiments on cavity cooling of silicon particles²⁰ and also to load an optical tweezer^21,22 and an ion trap.²³ In mass spectrometry, this technique has even been used on nanobiological matter, such as viruses and cells.²⁴ Such surface acceleration methods are effective, but it is still desirable to search for a tool that can control the number of particles, their directionality, release time, and velocity with good reproducibility. The method should allow particles to be prepared in vacuum with good control over their size and chemical composition.

In our present work, we explore femtosecond meltout as a promising tool for preparing individualized nanoparticles on demand, in buffer gas and in vacuum. The process has high directionality and ejects pristine nanospheres of well-defined, controllable size.²⁵ While nanosecond lasers are well-suited for ablating materials, femtosecond laser pulses have shown better controlled results for nanoparticle creation.²⁶ The short pulse duration minimizes thermal diffusion and thus defines a more confined target area. Only a few nanojoules of pulse energy are then required to create individual nanoparticles. Mode-locked lasers are also interesting as they can have a high mode quality, which is hard to achieve in Q-switched lasers. Since femtosecond laser inherently come with high repetition rates and because the ejection process occurs on the subnanosecond timescale, the particle launch rate is only limited by the accuracy and speed of the sample positioning.

In terms of materials, we focus on pure silicon nanoparticles for their ultra-low absorption and high polarizability at 1550 nm as well as gold nanoparticles because of their high mass density and their strong plasmon resonance. The dielectric function of silicon (⁠ $ε1550=12$⁠) is nearly six times greater than that of the more commonly used SiO₂ (⁠ $ε1550=2.1$⁠), resulting in a stronger light–particle coupling in optomechanics experiments.²⁷ The work functions of both gold (⁠ $W=5.38−5.45 eV$⁠) and silicon (⁠ $W=4.7−4.9 eV$⁠) allow these nanoparticles to be photo-ionized by 213 nm light (5.82 eV), available as the fifth harmonic of a Nd:YAG laser beam. This is promising for future quantum interference experiments with nanoparticles that rely on photodepletion gratings.^28,29

Prior studies found that the launch process depends on the details of the solid–liquid phase transition of thin layers. For gold, the solid phase is denser than the molten phase. The molten liquid therefore expands away from the supporting substrate. Thermoplastic deformation and surface tension then lead to the formation of a jet that can release one or two spherical nanoparticles from its tip,³⁰ as sketched in Fig. 1. If the laser pulse energy is too low, the jet freezes into a spire before the particle detaches. If the energy is too high, the droplet can break up into many fragments.

In contrast to gold, silicon is an anomalous liquid: the liquid phase is denser than the solid phase and the substrate shrinks when molten. This leads to the formation of a depression in the substrate. In the center of the depression a small silicon hill can still form due to surface tension and at sufficient laser energy, the hill transitions into a nanodroplet that detaches from the surface.³¹ 

Our setup, as shown in Fig. 1, is inspired by prior experiments on laser-induced backward transfer in air, which found intriguing applications in nanofabrication and nanoparticle printing.³¹ In our present realization, a laser (Light Conversion/Pharos) delivers pulses of $λ=515 nm$ wavelength and $τ=290 fs$ duration with up to $Ep=110 μJ$ of pulse energy from single shot up to a repetition rate of 50 kHz in a Gaussian beam of high mode quality, $M2=1.2$⁠.

We attenuate the pulses to 2–50 nJ before focusing them with an aspheric lens (⁠ $f=4.6 mm$⁠, NA = 0.55) to a submicrometer waist on the target substrate. Since the particle size depends on the thickness of the substrate,²⁵ we use a silicon-on-insulator (SOI) wafer, i.e., a 50 nm layer of silicon on 1 μm of SiO₂, on top of a 300 μm silicon wafer. Silicon is highly absorptive at 515 nm and can therefore be heated very fast beyond its melting point at $Tm=1687 K$⁠. SiO₂, however, is transparent at this wavelength and has a higher melting point (⁠ $Tm=1983 K$⁠). Therefore, it acts as a well-defined barrier that limits the amount of material that can be liquefied in a single pulse. The top layer may even be etched to a thickness of 30 nm, limiting the accessible target material, when the goal is to achieve smaller particle sizes.³² For gold, we have sputtered a 100–150 nm thick layer onto a glass substrate with a local smoothness on the nanometer scale.

Despite differences between materials, the overall formation of particles is always similar: At a laser fluence of I > 1 TW/cm², melting and surface tension lead to the ejection of a droplet that solidifies into a nanosphere. The craters in the target surface can be studied in situ using optical microscopy or ex situ using scanning electron microscopy. To image the size and distribution of the ejected nanoparticles, we mounted a quartz slide 10 μm below the target. While the laser beam remained fixed, the capture slide and the target substrate were translated together between the laser shots. For experiments in air, the focusing lens was also used for iSCAT imaging. After deposition in vacuum, the slide was extracted and coated with a few nanometer thick gold film before being subjected to scanning electron microscopy. To monitor the dynamics of the particles, we remove the collector slide and observe the light the particles scatter in transit through a high-finesse cavity underneath the substrate. This symmetric cavity with a linewidth of about $Δν=300 kHz$⁠, mirror curvature $Rc=10 cm$⁠, and mirror separation $Lc=2.1 cm$ has a waist of $wc=120 um$ and a finesse of $F≃2×104$⁠. We stabilize an infrared diode laser with $λc=1550 nm$ to this cavity using a side-of-fringe lock. The light that is scattered by a particle in transit is captured by a multimode fiber with a core diameter of 600 μm, placed at 500 μm horizontal distance to the center of the cavity.

Figure 2 shows the material response to laser pulses in different energy regimes. The SOI wafer was irradiated by individual femtosecond pulses with an energy of 4.5–9 nJ. We can correlate a characteristic surface defect in the target (top row) with the nanoparticle ejected under similar settings (bottom row) and we find that for a fixed focal waist, changing the pulse energy by a few nanojoules can change the yield and the particle size substantially. This is consistent with observations made for nanoprinting in air.³¹ 

We assess the vertical (forward) particle velocity $vz,TOF=d/TTOF$ by measuring the time-of-flight $TTOF$ between the laser pulse and the particle arrival at the center of the cavity mode at a distance d = 500 μm. Since any delay in the ejection process would mimic a lower particle speed, we additionally determine the transit velocity $vz,τz=2wc/τz$ from the time τ_z it takes to cross the cavity profile, indicated by the shaded area in Fig. 3(a). The latter is independent of the position along the y axis and largely independent of the x position. We then derive the horizontal velocity $vx=λc/2τx$ from the time τ_x [solid bar in Fig. 3(a)] it takes a particle to cross two neighboring cavity nodes, separated by $λc/2$⁠. The distribution of horizontal and the vertical velocities provides us with an estimate for the divergence angle of the emission process, $ϑ=arctan(vx/vz)$⁠.

In order to measure the initial particle velocities, we have conducted experiments at a pressure of $10−2$ mbar, where buffer gas collisions can be neglected on the short path from the target to the infrared cavity. By varying the pulse energy, we typically produce nanoparticles with a radius of $r=80–200 nm$ from an SOI wafer with a device layer thickness of 50 nm. Performing many dozens of experiments for silicon and gold, we extracted the cavity response, as shown in Fig. 3(a). From this, we obtained information on the particle forward velocity for silicon (gold), shown in Figs. 3(b) and 3(c), as well as the fly-through angle, shown in Fig. 3(d). We find a median angle of $ϑ=1.5°$⁠.

To assess the directionality of the nanoparticle launch, we show in Fig. 4 the particle transfer of silicon nanoparticles at a base pressure of $p=10−2$ mbar. Panels (a) and (b) show that the crater distribution in the target is copied to the particle pattern on the capture slide. Panels (a) and (b) are SEM images after experiments in vacuum (⁠ $10−2$ mbar), while panels (c) and (d) are in situ images using iSCAT microscopy in air. By comparing the number of shots and the number of collected particles, we find a launch and transfer of individual nanoparticles with a probability of $η≃90 %$⁠. However, even at only a few nanojoules per pulse, nanoparticle doublets may be occasionally ejected. We also find a distribution of smaller nanoparticles arranged around the craters on the target, seen as white dots in Figs. 4(a) and 4(c).

We have demonstrated the efficient and directed launch of pure silicon and gold nanoparticles using low-energy ultrashort laser pulses, also in vacuum. We expect the particles to be initially charged because of their initial temperature beyond the melting points as well as the potential for plasma formation and surface patch charges.

This makes the method compatible with levitated optomechanics in ion traps.^23,33 The initial nanoparticle velocities are still too high for direct loading of an optical tweezer in high vacuum. However, the flexibility in choosing the particle size, the directed character, and the compatibility with any pressure in such experiments make femtosecond meltout an interesting alternative to established techniques. The capability of handling pristine or doped silicon is expected to become an interesting feature in future experiments as silicon responds well to deep ultraviolet charge control. While meltout generates hot nanoparticles from the start, any ejected particle will quickly thermalize under the conditions of the subsequent experiment, i.e., to the vacuum chamber's surface temperature in an ion trap in high vacuum or to the steady-state equilibrium between heating and black body radiation inside an optical tweezer.

The method requires only very small amounts of starting material, it keeps the experiment clean, and it opens avenues for work with pristine or doped silicon. While nanoparticles in the range $108−1010$ Da are easily produced, future experiments shall also explore the possibility of generating particles below 10⁷ Da—on demand, from smaller sample volumes and with multi-kilohertz repetition rates.

We acknowledge financial support by the Austrian Science Funds within Project No. FWF P32543-N, by the Gordon & Betty Moore Foundation within Project No. 10771, and by the Office of Naval Research Global within Project No. N62909-23-1-2029.

We are thankful for the contribution toward early experiments and ideas by Stefan Kuhn and James Millen as well as helpful scientific discussions with Boris Chichkov.

The authors have no conflicts to disclose.

Philipp Rieser: Conceptualization (supporting); Investigation (lead); Methodology (supporting); Writing – original draft (equal). Nafia Rahaman: Investigation (equal). Felix Donnerbauer: Investigation (equal); Methodology (supporting). Stefan Putz: Methodology (supporting); Resources (lead). Armin Shayeghi: Conceptualization (supporting); Methodology (supporting); Supervision (supporting). Stephan Troyer: Conceptualization (supporting); Formal analysis (lead); Investigation (equal); Methodology (lead); Writing – original draft (equal). Markus Arndt: Conceptualization (lead); Supervision (lead); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.